Kumar Sangakkara rang the five-minute bell ahead of the start of the first day.
Cook won the toss and had no hesitation in batting first.
Alex Hales (18) and Cook gave England a steady start and scored 56 runs for the first wicket before the former was dismissed by Rangana Herath.
Alastair Cook was presented with a silver bat to commemorate his 10,000 Test just ahead of the start.
Sri Lanka fought back just before lunch to reduce England to 74 for 3 to win the first session.
Jonny Bairstow and Alastair Cook (85) rebuild for England in the second session with an 80-run stand before the latter was trapped in front by Pradeep just before tea to leave the hosts at 165 for 5.
Jonny Bairstow (107 not out) scored his first Test ton at Lord's and helped England end the day on 279 for 6.